Suppose that a is a square matrix with characteristic polynomial (λ − 3)2(λ − 6)3(λ + 1). (a) what are the dimensions of a? (give n such that the dimensions are n × n.) n = 6 correct: your answer is correct. (b) what are the eigenvalues of a? (enter your answers as a comma-separated list.) λ = 3,6,−1 correct: your answer is correct. (c) is a invertible?

The problem statement gives the correct answers for parts (a) and (b). The total number of roots of the characteristic polynomial is the dimension of the matrix: 6. The eigenvalues are the zeros of the characteristic polynomial, 3 (multiplicity 2), 6 (multiplicity 3), and -1.

(c) The matrix is not invertible when one or more eigenvalues is zero. None of yours are zero, so the matrix is invertible.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

sorry i just need to anwers this to get points

step-by-step explanation: